Improving the performance of primal--dual interior-point method in inverse conductivity problems

Abstract

This study improves the performance of primal--dual interior-point method in inverse conductivity problems via replacing the conventional, complicatedly calculated scalar regularization parameter with a diagonal matrix termed ``multi-regularization parameter matrix'' here. The solution of the PD--IPM depends considerably on the choice of the regularization parameter. Calculation of the optimal regularization parameter, which yields the most accurate solution, is not simple due to the long iterative nature of the algorithm. The objective optimization, which is implemented by minimizing error in the solutions over an extensive range of the regularization parameters, yields the most accurate solution that can be achieved, although this method is not applicable in reality due to lack of knowledge about the actual conductivity field. However, the modified algorithm not only solves the problem independently using the regularization parameter, but also increases the accuracy of the solution, as well as its sharpness in comparison to the objective optimization.